## Why does the presence of tension reinforcement lead to increasing deflection in concrete structures?

In BS8110 a modification factor is applied to span/depth ratio to take into account the effect of tension reinforcement. In fact, deflection of concrete structure is affected by the stress and the amount of tension reinforcement.

To illustrate their relationship, let’s consider the following equation relating to beam curvature:

**Curvature = 1/r = e/(d-x) **

where r = radius of curvature

e = tensile strain in tension reinforcement

d = effective depth

x = depth of neutral axis

Provided that the tensile strain in tension reinforcement remains constant, the curvature of concrete structure increases with the depth of neutral axis. It is observed that the depth of neutral axis rises with tension steel ratio. Therefore, the curvature of concrete section is directly proportional to the tension steel ratio. In addition, the larger value of the depth of neutral axis enhances increased area of concrete compression so that the effect of creep on deflection appears to become significant.

*This question is taken from book named – A Self Learning Manual – Mastering Different Fields of Civil Engineering Works (VC-Q-A-Method) by Vincent T. H. CHU.*